According to Smale's Paradox it is possible to turn a sphere inside out (in 3D space) without creating a crease in the material of the sphere. The material must be able to pass through itself. This is a pretty abstruse theory though it seems simple. It's all about turning numbers and waves! But then again, I'm not a differential topologist.
Topology is the study of the shape of things (in a nutshell). Some would say it's actually a type of botany, but that seems more like a joke to me. Famous topologists include Mobius, Klien, and Boy. Mobius is responsible for the Mobius strip, which is basically you're belt but with a twist. Topologists have even inspired some poetry, such as "Mobius-strip Tease" by A.D. Hope.
To quote:
"Four Mobius strips brought my plan to fruition
Ingeniously joined by original sin;
If you rise to the urgings of your male intuition,
you'll find yourself out every time you go in"
Oh ha ha, it's dirty and mathematical. Math can be pretty vulgar though. There have been mathematical proofs to show that women are the root of all evil, and that hell is indeed exothermic. Both of these are interesting arguments.
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